Title: Extremal Energy Models and Global Optimization

The objective of global optimization (GO) is to find the absolutely best solution of nonlinear decision models that often have multiple - local and global - optima.

Extremal energy (point configuration) models in applied mathematics, physics, computational chemistry, biology, and other areas provide a practically important, as well as numerically challenging area to test and apply GO strategies.

In these models, the 'optimal' arrangement of a finite - possibly large - number of points is sought, according to a certain criterion function. Additional constraints (e.g., regarding a surface all points have to belong to) may also be present.

Such models are typically characterized by an exponentially increasing number of local energy minima. The issue of finding suitable solution strategies to produce globally optimized configurations (for large, non-trivial configurations, within a reasonable effort) has been open for decades.

In this talk, first, we review several frequently used energy model forms. Then some key mathematical observations and results are summarized. This is followed by a discussion related to model formulations as a (corresponding) GO problem, and by a concise review of relevant GO models and solution strategies.

For illustration, LGO - an integrated model development and solver system for analyzing and visualizing GO problems - will be applied to solve (smaller, yet non-trivial) instances of several energy models. A summary of numerical results - reported in details elsewhere - will also be presented.

We conclude by discussing the broad applicability of GO to this area, including far-reaching possibilities for energy model generalizations and extensions.